We examine the complementary types of motion induced by the time-dependent mean field and the related residual interaction in the frame of quasispin systems. The time-dependent Hartree-Fock law of motion is used to generate an instantaneous basis, where the residual interaction induces transitions that deviate the exact motion with respect to the simple Slater determinant evolution. Geometric images of both kinds of dynamics are given and definite time scales are extracted for the validity of the time-dependent Hartree-Fock description, its second order correction, and the building up of a noticeable relative polarization of the exact wave function. It is seen that in addition to the time-dependent Hartree-Fock motion over the Bloch sphere, the exact dynamics contains an "inwards" component as well as additional rotations.

NUCLEAR STRUCTURE Time-dependent Hartree-Fock; moving basis; residual interaction; complementary motions; quasispin systems; Slater determinant; time scales; rotations and nonrotations on Bloch sphere; polarization.

The mass-doublet-scale based energy of the 6129-keV $\gamma$ ray of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is reevaluated in light of a recent determination of the deuteron binding energy. The result is 6129.142 ± 0.032 keV. No serious descrepancy exists between this result and a recently measured value based on the wavelength (Au) standard.

RADIOACTIVITY ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, deduced energy of 6129-keV transition based on mass scale.

The mechanism of the reactions ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \alpha ){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ leading to the ${\frac{3}{2}}^{-}$ ground state and ${\frac{5}{2}}^{-}$ second excited state of ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ is studied using finite-range distorted-wave Born approximation with all one-step direct and exchange processes. By taking into account in detail the cluster structure of ${}_{}{}^{11}{}_{}{}^{}\mathrm{C}$ and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, the transition to the ${\frac{5}{2}}^{-}$ state which is a $j$ forbidden direct process can be explained well by the exchange process.

NUCLEAR REACTIONS ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He}, \alpha ){}_{}{}^{11}{}_{}{}^{}\mathrm{C}$, finite-range distorted-wave Born approximation analysis, direct and exchange processes, cluster structure.

Coulomb displacement energy calculations have been used to identify the lowest $T=1\mathrm{}$ states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$. The calculations have used existing shell-model wave functions and reproduce the experimental excitation energies, and so the change in level splitting. Applying a correction for systematic deviations increases the accuracy of the calculations to 20 keV and allows the proposal for four additional analog states.

NUCLEAR STRUCTURE $A=28\mathrm{}$, $T=1\mathrm{}$ triad; calculated Coulomb displacement energies. Shell-model wave functions.

We have calculated the Gamow-Teller strength of the ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}(p, n){}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}\left(1^{+}\right)$ reaction using the Kuo-Brown wave function. This shell model calculation together with the $\Delta$ isobar quenching mechanism accounts for the Gamow-Teller strength.

NUCLEAR STRUCTURE Shell model, reaction matrix, GT strength, $\Delta$ isobar polarization.

It is pointed out that the coupling constants and form factors of the "cloudy" (a chiral) bag model are a special case of the quark pairing mechanism for meson exchanges, where the quark reflections are restricted to the hadronic surface. A bag model formula for the pion decay constant $f$ results from a comparison of $g_{\pi \mathrm{NN}}$ from both models.

NUCLEON STRUCTURE Pion-baryon coupling constants, form factors, at low $q$. Comparison of results from chiral bag model and quark pairing mechanism.

The rapid descent of the fusion cross section for lighter heavy-ion systems at higher energies is interpreted in terms of a fusion entry line based on a new concept of the critical distance between heavy ions. This model reproduces well experimental data with one parameter; $\hslash {\omega }_d=(0.70\mathrm{}\pm 0.05)40A^{-\frac{1}{3}}$. The appearance of an angular momentum window in incomplete fusions is demonstrated for $\alpha$+${}_{}{}^{233}{}_{}{}^{}\mathrm{U}$.

NUCLEAR REACTIONS Heavy ion reactions, fusion, critical distance, angular momentum window in incomplete fusion.

In this paper we propose a microscopic method of calculating Pauli-corrected intercluster interactions. The method is based on a microscopic Hamiltonian which contains the influence of the Pauli principle and from which the corresponding intercluster potentials are derived. This method overcomes the difficulties of the inclusion of the Pauli principle in systems of more than two clusters which occur in the resonating group method, orthogonality condition model, projection method, and the fish bone model. Moreover, it allows the investigation of the influence of the microscopic parameters in different systems and the examination of the on- and off-shell behavior of the intercluster forces in a consistent way.

NUCLEAR REACTIONS Composite particle interaction, $N$-cluster theory, nuclear fragments, scattering theory.

A systematic study of the charge distribution for bremsstrahlung-induced photofission of ${}_{}{}^{235}{}_{}{}^{}\mathrm{U}$ and ${}_{}{}^{238}{}_{}{}^{}\mathrm{U}$ with the end point energies ranging from 12 to 30 MeV was performed using direct $\gamma$-ray spectrometry of irradiated uranium samples or of fission product catcherfoils, and also employing chemical separation techniques. For both fissioning systems the width of the charge distribution was found to be practically independent of the average excitation energy and the values obtained are in very good agreement with those reported in the literature for low-energy fission. The deviation of the most probable charge $Z_p$ from the unchanged charge density value $Z_{\mathrm{UCD}}$ as a function of the fragment mass shows the influence of the 50-proton shell in the charge distributions and a higher charge-to-mass ratio of the light fragments independent of the compound nucleus excitation energy. For the necessary conversion of postneutron into preneutron masses, neutron emission curves, $\nu \left(m^{*}\right)$, were deduced from previously measured postneutron and provisional mass distributions. Calculations following the scission-point model of Wilkins et al. and the predictions of the empirical relation of Nethaway reproduce very well the experimentally determined $Z_p$ behavior, except in the mass region affected by the $Z=50\mathrm{}$ closed shell.

NUCLEAR REACTIONS, FISSION ${}_{}{}^{235,238}{}_{}{}^{}\mathrm{U}(\gamma , F)$, $E_{\gamma max}=12, 15, 20, 30$ MeV; measured product $\gamma$-ray spectra; deduced charge distributions, width, and most probable charges; calculated $\nu \left(m^{*}\right)$ from measured provisional and postneutron mass distributions.

This paper investigates the ability of a cluster expansion to construct accurate approximate solutions for the three-body problem where the pairwise interactions are nonseparable potentials. Our approach is to employ the Karlsson-Zeiger integral equation formalism and the decoupling scheme of Bollé and Kuzmichev to construct an effective intercluster potential for the three-body problem. This effective potential takes into account all virtual excitations of the three-body breakup channel. It is found that a simplifying approximation to the effective potential, utilizing only the first few terms of a cluster expansion, yields accurate numerical solutions in the bound state and low energy elastic scattering sectors. In this paper we give numerical results for a system composed of three bosons interacting via the $S$-wave projection of a Yukawa potential.

NUCLEAR REACTIONS Three-body problem. Cluster expansion, local interactions.

Cross sections for ($p, \mathrm{pd}$) and ($p, \mathrm{pt}$) reactions at 101.3 MeV and ($\alpha , \alpha d$), ($\alpha , \alpha t$), and ($\alpha , \alpha {}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions at 139.2 MeV have been measured for an ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ target. Distorted wave impulse approximation analyses of the data yield spectroscopic factors for the proton induced reactions which are comparable to shell model estimates. However, the alpha induced reactions yield values up to two orders of magnitude larger. The relationship of these results to similar results for alpha knockout reactions is discussed.

NUCLEAR REACTIONS ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(p, pd)$, ($p, \mathrm{pt}$), $E=101.3\mathrm{}$ MeV, ($\alpha , \alpha d$), ($\alpha , \alpha t$), ($\alpha , \alpha {}_{}{}^3{}_{}{}^{}\mathrm{He}$), $E=139.2\mathrm{}$ MeV; measured $\sigma (E_1, E_2, {\theta }_1, {\theta }_2)$; DWIA analysis, deduced spectroscopic factors.

Formulation of the zero-energy Faddeev-type scattering equations in configuration space is discussed. Numerical solutions are obtained using spline techniques. Scattering lengths are calculated for the $s$-wave $\mathrm{NN}$ interaction models of Malfliet and Tjon; comparison with previously published results and Kohn variational estimates are made. Faddeev amplitudes and Schrödinger wave functions are plotted. Significant features of the configuration space solutions are identified.

NUCLEAR REACTIONS ${}_{}{}^2{}_{}{}^{}\mathrm{H}(n, n){}_{}{}^2{}_{}{}^{}\mathrm{H}$, $E=0\mathrm{}$ MeV; $n-d$ scattering lengths; configuration space Faddeev calculation.

The integrated and bremsstrahlung-weighted cross sections have been calculated including the one-pion-exchange contributions to the charge density for the Paris, super-soft-core, Yale, Hamada-Johnston, and modified Hamada-Johnston potentials. The contribution of the two-meson exchange to the integrated cross section has been estimated. For velocity independent potentials the change in the enhancement factor due to the meson exchange is found to be approximately the same, but it is a little larger for the velocity dependent (Paris) potential. It is found that contrary to the claim made in the literature the integrated cross section cannot distinguish between the various two-nucleon potentials.

NUCLEAR REACTIONS $d(\gamma , p)n$, calculated integrated and bremsstrahlung-weighted cross sections; included one- and two-pion exchange contribution.

The neutron capture cross sections of ${}_{}{}^{178,179,180}{}_{}{}^{}\mathrm{Hf}$ were measured in the energy range 2.6 keV to 2 MeV. The average capture cross sections were calculated and fitted in terms of strength functions. Resonance parameters for the observed resonances below 10 keV were determined by a shape analysis. Maxwellian averaged capture cross sections were computed for thermal energies $\mathrm{kT}$ between 5 and 100 keV. The cross sections for $kT=30\mathrm{}$ keV were used to determine the population probability of the $8^{-}$ isomeric level in ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ by neutron capture as (1.24±0.06)% and the $r$-process abundance of ${}_{}{}^{180}{}_{}{}^{}\mathrm{Hf}$ as 0.0290 (Si ≡ ${10}^6$). These quantities served to analyze $s$- and $r$-process nucleosynthesis of ${}_{}{}^{180}{}_{}{}^{}\mathrm{Ta}$.

NUCLEAR REACTIONS ${}_{}{}^{178,179,180}{}_{}{}^{}\mathrm{Hf}(n, \gamma )$, $E=2.6-2000\mathrm{}$ keV, measured $\sigma \mathrm{}\left(E\right)\mathrm{}$, deduced ${}_{}{}^{178,179,180}{}_{}{}^{}\mathrm{Hf}$ resonance parameters, strength functions, average level spacings, Maxwellian averaged capture cross sections, analysis of $s$- and $r$-process nucleosynthesis of ${}_{}{}^{180}{}_{}{}^{}\mathrm{Ta}$.

Nuclear states of ${}_{}{}^{79}{}_{}{}^{}\mathrm{Kr}$ were studied through the ${}_{}{}^{78}{}_{}{}^{}\mathrm{Se}(\alpha , 3n)$ reaction at an energy of 45 MeV. Excitation functions, $\gamma$-ray angular distributions, and $\gamma -\gamma$ coincidences were performed. Three bands based on the g.s. ($\frac{1}{2^{-}}$), 147.1 keV ($\frac{5}{2^{-}}$), and 129.7 keV ($\frac{7}{2^{+}}$) states were identified. Leading order analysis and quasiparticle-plus-rotor model calculations were performed. A good overall agreement was found between the experimental data and the theoretical predictions.

NUCLEAR REACTIONS ${}_{}{}^{78}{}_{}{}^{}\mathrm{Se}(\alpha , 3n)$, $E=30-55\mathrm{}$ MeV; measured $\sigma (E, E_{\gamma }, \theta )$, $E_{\gamma }$, $I_{\gamma }$, $\gamma -\gamma$ coin. ${}_{}{}^{79}{}_{}{}^{}\mathrm{Kr}$ deduced levels $J$. Enriched targets.